Surveying
If θ and δ be the latitude of an observer and declination of a heavenly body respectively, the upper culmination of the body will be south of zenith if its zenith distance, is

θ - δ
½ (θ - δ)
θ + δ
δ - θ

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Surveying
The error due to eccentricity of inner and outer axes can be eliminated by

reading both verniers and taking the mean of the two
taking mean of several readings distributed over different portions of the graduated circle
double sighting
taking both face observations and taking the mean of the two

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